This project must be done by individuals.

*For the purposes of this exercise,
you may treat the neutrino and anti-neutrino
as massless.
In other words, they have no rest mass,
but they do have energy and they do carry momentum.
*

An isolated neutron is not stable. It decays into three particles:

- a proton
- an electron
- an anti-neutrino

Fill in the table below. Note that I have set the mass of the anti-neutrino to be zero, which is a simplifying approximation.

particle mass (kg) mass (MeV/c^2) --------------------------------------------------- neutron proton electron anti-neutrino 0 0 ---------------------------------------------------

- What is the difference in mass between the initial neutron and the final products?
- How much energy does this correspond to?
Assume that the neutron is initially motionless. Suppose that after the decay, the proton is likewise motionless. The anti-neutrino, of course, can't be motionless, so it flies off at the speed of light to the right, in the positive x-direction.

- Draw a pair of pictures showing the "Before" and "After" arrangement of the particles, and their motions.
- Write an equation for the total energy of the particles in the "After" set.
- Write an equation for the total momentum of the particles in the "After" set.
- How fast must the electron fly away from the proton? Express your answer as a fraction of the speed of light.

*
(Hint: the algebra in this problem isn't trivial. Feel free to
solve for the electron's speed numerically, as long as you
describe your method.)
*

Copyright © Michael Richmond. This work is licensed under a Creative Commons License.